Wan Wen, Pei Xin-Yan, Grant Steven, Birch Jeffrey B, Felthousen Jessica, Dai Yun, Fang Hong-Bin, Tan Ming, Sun Shumei
Department of Biostatistics, Virginia Commonwealth University, Richmond, VA 23298, USA.
Department of Internal Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA.
Biom J. 2017 Jan;59(1):9-24. doi: 10.1002/bimj.201500021. Epub 2016 May 17.
Few articles have been written on analyzing three-way interactions between drugs. It may seem to be quite straightforward to extend a statistical method from two-drugs to three-drugs. However, there may exist more complex nonlinear response surface of the interaction index (II) with more complex local synergy and/or local antagonism interspersed in different regions of drug combinations in a three-drug study, compared in a two-drug study. In addition, it is not possible to obtain a four-dimensional (4D) response surface plot for a three-drug study. We propose an analysis procedure to construct the dose combination regions of interest (say, the synergistic areas with II≤0.9). First, use the model robust regression method (MRR), a semiparametric method, to fit the entire response surface of the II, which allows to fit a complex response surface with local synergy/antagonism. Second, we run a modified genetic algorithm (MGA), a stochastic optimization method, many times with different random seeds, to allow to collect as many feasible points as possible that satisfy the estimated values of II≤0.9. Last, all these feasible points are used to construct the approximate dose regions of interest in a 3D. A case study with three anti-cancer drugs in an in vitro experiment is employed to illustrate how to find the dose regions of interest.
关于分析药物之间的三方相互作用的文章很少。将统计方法从两种药物扩展到三种药物似乎相当简单。然而，与双药研究相比，在三药研究中，相互作用指数（II）的响应面可能更复杂，在药物组合的不同区域散布着更复杂的局部协同和/或局部拮抗作用。此外，对于三药研究，不可能获得四维（4D）响应面图。我们提出了一种分析程序来构建感兴趣的剂量组合区域（例如，II≤0.9的协同区域）。首先，使用模型稳健回归方法（MRR），一种半参数方法，来拟合II的整个响应面，这允许拟合具有局部协同/拮抗作用的复杂响应面。其次，我们多次运行改进的遗传算法（MGA），一种随机优化方法，使用不同的随机种子，以收集尽可能多的满足II≤0.9估计值的可行点。最后，所有这些可行点用于在三维空间中构建近似的感兴趣剂量区域。通过一个在体外实验中使用三种抗癌药物的案例研究来说明如何找到感兴趣的剂量区域。
